Тұрақты толқын құбылысы

Wave that remains in a constant position

In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect to time, and the oscillations at different points throughout the wave are in phase. The locations at which the absolute value of the amplitude is minimum are called nodes, and the locations where the absolute value of the amplitude is maximum are called antinodes. Standing waves were first described scientifically by Michael Faraday in 1831. Faraday observed standing waves on the surface of a liquid in a vibrating container. Franz Melde coined the term "standing wave" (German: stehende Welle or Stehwelle) around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings. This phenomenon can occur because the medium is moving in the direction opposite to the movement of the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. The most common cause of standing waves is the phenomenon of resonance, in which standing waves occur inside a resonator due to interference between waves reflected back and forth at the resonator's resonant frequency. For waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy.

As an example of the first type, under certain meteorological conditions standing waves form in the atmosphere in the lee of mountain ranges. Such waves are often exploited by glider pilots. Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom. A requirement for this in river currents is a flowing water with shallow depth in which the inertia of the water overcomes its gravity due to the supercritical flow speed (Froude number: 1.7 – 4.5, surpassing 4.5 results in direct standing wave) and is therefore neither significantly slowed down by the obstacle nor pushed to the side. Many standing river waves are popular river surfing breaks.

This section considers representative one and two dimensional cases of standing waves. First, an example of an infinite length string shows how identical waves traveling in opposite directions interfere to produce standing waves. Next, two finite length string examples with different boundary conditions demonstrate how the boundary conditions restrict the frequencies that can form standing waves. Next, the example of sound waves in a pipe demonstrates how the same principles can be applied to longitudinal waves with analogous boundary conditions. Standing waves can also occur in two or three dimensional resonators. With standing waves on two dimensional membranes such as drumheads, illustrated in the animations above, the nodes become nodal lines, lines on the surface at which there is no movement, that separate regions vibrating with opposite phase. These nodal line patterns are called Chladni figures. In three dimensional resonators, such as musical instrument sound boxes and microwave cavity resonators, there are nodal surfaces. This section includes a two dimensional standing wave example with a rectangular boundary to illustrate how to extend the concept to higher dimensions.

If the two oppositely moving traveling waves are not of the same amplitude, they will not cancel completely at the nodes, the points where the waves are 180° out of phase, so the amplitude of the standing wave will not be zero at the nodes, but merely a minimum. Standing wave ratio (SWR) is the ratio of the amplitude at the antinode (maximum) to the amplitude at the node (minimum). A pure standing wave will have an infinite SWR. It will also have a constant phase at any point in space (but it may undergo a 180° inversion every half cycle). A finite, non zero SWR indicates a wave that is partially stationary and partially travelling. Such waves can be decomposed into a superposition of two waves: a travelling wave component and a stationary wave component. An SWR of one indicates that the wave does not have a stationary component – it is purely a travelling wave, since the ratio of amplitudes is equal to 1. A pure standing wave does not transfer energy from the source to the destination. However, the wave is still subject to losses in the medium. Such losses will manifest as a finite SWR, indicating a travelling wave component leaving the source to supply the losses. Even though the SWR is now finite, it may still be the case that no energy reaches the destination because the travelling component is purely supplying the losses. However, in a lossless medium, a finite SWR implies a definite transfer of energy to the destination.

One easy example to understand standing waves is two people shaking either end of a jump rope. If they shake in sync the rope can form a regular pattern of waves oscillating up and down, with stationary points along the rope where the rope is almost still (nodes) and points where the arc of the rope is maximum (antinodes).

Standing waves are also observed in physical media such as strings and columns of air. Any waves traveling along the medium will reflect back when they reach the end. This effect is most noticeable in musical instruments where, at various multiples of a vibrating string or air column's natural frequency, a standing wave is created, allowing harmonics to be identified. Nodes occur at fixed ends and anti nodes at open ends. If fixed at only one end, only odd numbered harmonics are available. At the open end of a pipe the anti node will not be exactly at the end as it is altered by its contact with the air and so end correction is used to place it exactly. The density of a string will affect the frequency at which harmonics will be produced; the greater the density the lower the frequency needs to be to produce a standing wave of the same harmonic.

Standing waves are also observed in optical media such as optical waveguides and optical cavities. Lasers use optical cavities in the form of a pair of facing mirrors, which constitute a Fabry–Pérot interferometer. The gain medium in the cavity (such as a crystal) emits light coherently, exciting standing waves of light in the cavity. The wavelength of light is very short (in the range of nanometers, 10−9 m) so the standing waves are microscopic in size. One use for standing light waves is to measure small distances, using optical flats.

Interference between X ray beams can form an X ray standing wave (XSW) field. Because of the short wavelength of X rays (less than 1 nanometer), this phenomenon can be exploited for measuring atomic scale events at material surfaces. The XSW is generated in the region where an X ray beam interferes with a diffracted beam from a nearly perfect single crystal surface or a reflection from an X ray mirror. By tuning the crystal geometry or X ray wavelength, the XSW can be translated in space, causing a shift in the X ray fluorescence or photoelectron yield from the atoms near the surface. This shift can be analyzed to pinpoint the location of a particular atomic species relative to the underlying crystal structure or mirror surface. The XSW method has been used to clarify the atomic scale details of dopants in semiconductors, atomic and molecular adsorption on surfaces, and chemical transformations involved in catalysis.

Standing waves can be mechanically induced into a solid medium using resonance. One easy to understand example is two people shaking either end of a jump rope. If they shake in sync, the rope will form a regular pattern with nodes and antinodes and appear to be stationary, hence the name standing wave. Similarly a cantilever beam can have a standing wave imposed on it by applying a base excitation. In this case the free end moves the greatest distance laterally compared to any location along the beam. Such a device can be used as a sensor to track changes in frequency or phase of the resonance of the fiber. One application is as a measurement device for dimensional metrology.

Standing surface waves on the Earth are observed as free oscillations of the Earth.

The Faraday wave is a non linear standing wave at the air liquid interface induced by hydrodynamic instability. It can be used as a liquid based template to assemble microscale materials.

A seiche is an example of a standing wave in an enclosed body of water. It is characterised by the oscillatory behaviour of the water level at either end of the body and typically has a nodal point near the middle of the body where very little change in water level is observed. It should be distinguished from a simple storm surge where no oscillation is present. In sizeable lakes, the period of such oscillations may be between minutes and hours, for example Lake Geneva's longitudinal period is 73 minutes and its transversal seiche has a period of around 10 minutes, while Lake Huron can be seen to have resonances with periods between 1 and 2 hours. See Lake seiches.